TY - JOUR
T1 - Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein–Gordon equation and numerical comparisons
AU - Muda, Y.
AU - Akbar, F. T.
AU - Kusdiantara, R.
AU - Gunara, B. E.
AU - Susanto, H.
N1 - Funding Information:
YM thanks MoRA ( Ministry of Religious Affairs ) Scholarship of the Republic of Indonesia for a financial support. The research of FTA and BEG is supported by PDUPT Kemenristekdikti 2018. RK gratefully acknowledges financial support from Lembaga Pengelolaan Dana Pendidikan (Indonesian Endowment Fund for Education) (Grant No. – Ref: S-34/LPDP.3/2017 ). The authors are grateful to the four reviewers for their comments that improved the quality of the manuscript.
Funding Information:
YM thanks MoRA (Ministry of Religious Affairs) Scholarship of the Republic of Indonesia for a financial support. The research of FTA and BEG is supported by PDUPT Kemenristekdikti 2018. RK gratefully acknowledges financial support from Lembaga Pengelolaan Dana Pendidikan (Indonesian Endowment Fund for Education) (Grant No. – Ref: S-34/LPDP.3/2017). The authors are grateful to the four reviewers for their comments that improved the quality of the manuscript.
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/4/10
Y1 - 2019/4/10
N2 - We consider a damped, parametrically driven discrete nonlinear Klein–Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schrödinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates. Furthermore, we prove the local and global existence of solutions to the discrete nonlinear Schrödinger equation. To illustrate the main results, we consider numerical simulations showing the dynamics of errors made by the discrete nonlinear equation. We consider two types of initial conditions, with one of them being a discrete soliton of the nonlinear Schrödinger equation, that is expectedly approximate discrete breathers of the nonlinear Klein–Gordon equation.
AB - We consider a damped, parametrically driven discrete nonlinear Klein–Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schrödinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates. Furthermore, we prove the local and global existence of solutions to the discrete nonlinear Schrödinger equation. To illustrate the main results, we consider numerical simulations showing the dynamics of errors made by the discrete nonlinear equation. We consider two types of initial conditions, with one of them being a discrete soliton of the nonlinear Schrödinger equation, that is expectedly approximate discrete breathers of the nonlinear Klein–Gordon equation.
KW - Discrete breather
KW - Discrete Klein–Gordon equation
KW - Discrete nonlinear Schrödinger equation
KW - Discrete soliton
KW - Small-amplitude approximation
UR - https://www.scopus.com/pages/publications/85060858874
U2 - 10.1016/j.physleta.2019.01.047
DO - 10.1016/j.physleta.2019.01.047
M3 - Article
AN - SCOPUS:85060858874
SN - 0375-9601
VL - 383
SP - 1274
EP - 1282
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 12
ER -